[35.05] Solar-Cycle Variation of Polarity Inversion

H. P. Jones (NASA/GSFC)

Multi-scale polarity inversion maps are constructed from National Solar
Observatory/Kitt Peak magnetograms for periods coinciding with those
used by Harvey (1993, PhD Thesis, Utrecht University). The motivation
for this analysis stems from earlier work on a small sample which
suggested that neutral-line "length" varies as a power of the scale
used to determine the polarity inversion loci and that only the
amplitude, not the exponent, varies between maximum and minimum phases
of the solar cycle. Harvey observed similar behavior in the areal
distribution of new bipolar regions, and a plausible hypothesis is that
neutral line length vs. scale is a mapping of this areal distribution,
i.e., an efficient way to count bipoles. Broadly speaking, the
behavior of neutral line length vs. scale is confirmed from this more
extensive sample; the curves from many days at either minimum or
maximum are tightly clustered and are nearly parallel on log-log
plots. Emperically, if one represents the areal distribution of new
bipolar regions as a function of time and area as
\begindisplaymath
n(t,A) \sim f(t)g(A),
\enddisplaymath
then neutral-line length, \ell, varies with scale, s, as
\begindisplaymath
\ell(s) \sim const*[g(s^2)/f(t)]^r
\enddisplaymath
where r \simeq 0.2. To explore whether this
relation has more than emperical significance, future work is planned
to compute neutral line maps from synthesized magnetograms based on
the superposition of known, prespecified distributions of dipoles.